Python Integer Produc Under Modulus

class mod_math:
    @staticmethod
    @njit
    def mod_prod1(factors: Iterable[int], modulus: int, start_with: int = 1, mechanism_specification: Union[bool, int, None] = None) -> int:
        """
        Computes the product of a set of factors modulo a given modulus.

        This function multiplies each factor in the iterable and continuously takes the result modulo the given modulus.
        It can optionally start the multiplication with an initial value and check for specific conditions on the intermediate product's value.


        Chained Generators and Dual StopIteration Behavior:

            When working with chained generators or when using coroutines, a seamless transition from one generator to the next is often desired.
            However, a challenge arises when a generator finishes its sequence: it raises a StopIteration exception.

            In typical scenarios, when consuming an iterable, a single StopIteration is expected to indicate the end of the sequence.
            However, this function employs a unique mechanism to deal with chained generators.
            Specifically, it expects two consecutive StopIteration exceptions to determine that the sequence has genuinely ended.

            - Chained Generators:
                Generators can be "chained" using libraries like itertools.chain(). This itertool can work for all generators.
                But it might not work for more advanced co-routines. Hence, this feature.

            - Double StopIteration Mechanism:
                This function handles chained generators by expecting two consecutive StopIteration exceptions as a fail-safe or double-confirmation to ensure that the sequence is truly finished.
                1. The first StopIteration: Indicates that a particular generator in the chain is exhausted.
                2. The second consecutive StopIteration: Confirms that there are no more chained generators left to process.

            - Benefit:
                This mechanism allows for efficient processing of chained generators without prematurely terminating the loop.
                It's particularly useful if the generator sequence's end isn't known in advance or if the sequence is dynamically created.

            - Considerations:
                * This mechanism assumes a certain structure for the input. It works best with chained generators but may result in unexpected behaviors with regular iterables.
                * Consuming an extra item from a generator may not always be side-effect-free. If the generator involves IO operations or other side effects, this mechanism might inadvertently trigger them.

            - Input Structure Assumption:
                This mechanism assumes a certain structure to the input, designed explicitly for chained generators.
                Using this function on standard iterables without such chaining might lead to unexpected behaviors.
                It's essential to be cautious and aware of the nature of the iterable being processed.

            - Potential Side Effects:
                The function may consume an extra item from a generator, which isn't always side-effect-free.
                Generators that involve IO operations, stateful computations, or other side effects might behave differently than expected.
                Triggering these operations inadvertently can lead to unexpected behaviors or states in the system.

            It's imperative to ensure that the nature and structure of the input iterable align with the expectations of this function, especially when relying on the Dual StopIteration mechanism.

        Parameters:

        - factors (Iterable[int]): The sequence of integers to be multiplied.
        - modulus (int): The modulus under which the multiplication is performed.
        - start_with (int, optional): The initial value from which the multiplication begins. Defaults to 1.
        - mechanism_specification (Union[bool, int, None], optional): Controls early exit behavior based on intermediate product values.
            - If True, the function returns immediately if the product becomes 0.
            - If False, the function keeps iterating over the factors until the product becomes 0.
                If the factors are exhausted, it will try reading two more times (expecting two consecutive 'StopIteration' exceptions) before terminating.
                This is designed to work efficiently with chained generators or coroutines, allowing a seamless transition from one generator to the next.
             -If an integer, the function returns immediately if the product matches this integer.
            - If None, simply multiplies all factors without any special checks.

        Returns:

        - int: The final product of the factors modulo the given modulus.

        Examples:

        - Without mechanism_specification (default behavior):
        >>> mod_math.mod_prod([2, 3, 4], 100)
        24
        >>> mod_math.mod_prod([2, 3, 4], 5)
        4

        - With mechanism_specification=True (returns immediately if product becomes 0):
        >>> mod_math.mod_prod([2, 3, 4], 10, mechanism_specification=True)
        4
        >>> mod_math.mod_prod([2, 3, 0, 4], 10, mechanism_specification=True)
        0

        - With mechanism_specification=False (keeps iterating until product is 0, or after two consecutive 'StopIteration' exceptions):
        >>> mod_math.mod_prod(iter([2, 3, 4]), 100, mechanism_specification=False)
        24
        >>> mod_math.mod_prod(iter([2, 3]), 10, mechanism_specification=False)
        6  # Assuming the iterable is consumed and two consecutive 'StopIteration' exceptions are raised.
        >>> mod_math.mod_prod(flatten([2, 3, [4, 5], 6]), 1000, mechanism_specification=False)
        720
        >>> mod_math.mod_prod(flatten([2, [3], [4, [5, 6]]]), 1000, mechanism_specification=False)
        720
        >>> mod_math.mod_prod(flatten([2, 3, [0, 5], 6]), 1000, mechanism_specification=False)
        0  # Even though nested, the 0 causes the product to become 0.
        >>> mod_math.mod_prod(flatten([2, [3], [0, [5, 6]]]), 1000, mechanism_specification=False)
        0  # A nested 0 results in an immediate 0 product.

        - With mechanism_specification set to a specific integer (returns immediately if product matches the integer):
        >>> mod_math.mod_prod([2, 3, 4], 100, mechanism_specification=24)
        24
        >>> mod_math.mod_prod([2, 3, 4, 5], 100, mechanism_specification=24)
        0  # Product does not match mechanism_specification, so final modulo result is returned.
        """

        product_running: int = start_with

        if mechanism_specification is True:
            for x_factor in factors:
                product_running *= x_factor
                product_running %= modulus
                if product_running == 0:
                    return 0

        elif mechanism_specification is False:
            factors_iter: Iterator[int] = iter(factors)
            while True:
                while (x_factor := next(factors_iter, None)) is not None:
                    product_running *= x_factor
                    product_running %= modulus
                    if product_running == 0:
                        return 0

                if (x_factor := next(factors_iter, None)) is not None:  # premature termination detected
                    product_running *= x_factor
                    product_running %= modulus
                    if product_running != 0:
                        continue

                break

        elif mechanism_specification is not None:  # i.e., an integer value
            for x_factor in factors:
                product_running *= x_factor
                product_running %= modulus
                if product_running == mechanism_specification:
                    return mechanism_specification

        else:
            # Performing the modulo operation as here doing is an effective way to avoid memory bloat from large integers.
            # This is especially important if the iterable can be long or if the numbers involved are large.
            # Keeping the value bounded prevents any unforeseen memory issues.
            for x_factor in factors:
                product_running *= x_factor
                product_running %= modulus

        return product_running

    @staticmethod
    @njit
    def mod_prod2(factors: Iterable[int], modulus: int, start_with: int = 1, mechanism_specification: Union[bool, int, None] = None) -> int:

        # ... [Docstring remains unchanged]

        product_running: int = start_with
        factors_iter: Iterator[int] = iter(factors)

        while True:
            try:
                x_factor = next(factors_iter)
                product_running *= x_factor
                product_running %= modulus

                # Check for early exits based on mechanism_specification
                if mechanism_specification is True and product_running == 0:
                    return 0
                if isinstance(mechanism_specification, int) and product_running == mechanism_specification:
                    return mechanism_specification

            except StopIteration:
                if mechanism_specification is False:
                    try:
                        # Check for another StopIteration to handle chained generators
                        x_factor = next(factors_iter)
                        product_running *= x_factor
                        product_running %= modulus
                    except StopIteration:
                        break
                else:
                    break

        return product_running